This dissertation investigates the application of computational intelligence methods in the
analysis of nonlinear chaotic systems in the framework of many known and newly designed
complex systems. Parallel comparisons are made between these methods. This provides insight
into the difficult challenges facing nonlinear systems characterization and aids in developing a
generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents,
information dimension and topological entropy. These metrics are implemented to characterize
the dynamic patterns of discrete and continuous systems. These metrics make it possible to
distinguish order from disorder in these systems. Steps required for computing Lyapunov
exponents with a reorthonormalization method and a group theory approach are formalized.
Procedures for implementing computational algorithms are designed and numerical results for
each system are presented.
The advance-time sampling technique is designed to overcome the scarcity of phase
space samples and the buffer overflow problem in algorithmic complexity measure estimation in
slow dynamics feedback-controlled systems.
It is proved analytically and tested numerically that for a quasiperiodic system like a
Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block.
It is concluded that a normalized algorithmic complexity measure can be used as a system
classifier. This quantity turns out to be one for random sequences and a non-zero value less than
one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their
normalized complexity approaches zero, while a faster deceasing rate is observed for periodic
responses.
Algorithmic complexity analysis is performed on a class of certain rate convolutional
encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence
indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases
with the increase of the encoder constraint length. This occurs in parallel with the increase of
error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it
is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence
manifests smaller algorithmic complexity with a larger free distance value.

Access

Unrestricted

Degree

Ph. D.;

Degree Program

Engineering and Applied Science;

Department

Dept. of Physics;

Major Professor

Ioup, George

Advisory Committee

Ioup, Juliette; Tang, Jinke; Charalampidis, Dimitrios;

Date Degree Awarded

2008-05-16;

Format

PDF

URL

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Rights

The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.